We introduce a new generation of PARSEC-COLIBRI stellar isochrones that include a detailed treatment of the thermally-pulsing asymptotic giant branch (TP-AGB) phase, and covering a wide range of initial metallicities (0.0001 < Z i < 0.06). Compared to previous releases, the main novelties and improvements are: use of new TP-AGB tracks and related atmosphere models and spectra for M and C-type stars; inclusion of the surface H+He+CNO abundances in the isochrone tables, accounting for the effects of diffusion, dredge-up episodes and hot-bottom burning; inclusion of complete thermal pulse cycles, with a complete description of the in-cycle changes in the stellar parameters; new pulsation models to describe the long-period variability in the fundamental and first overtone modes; new dust models that follow the growth of the grains during the AGB evolution, in combination with radiative transfer calculations for the reprocessing of the photospheric emission. Overall, these improvements are expected to lead to a more consistent and detailed description of properties of TP-AGB stars expected in resolved stellar populations, especially in regard to their mean photometric properties from optical to mid-infrared wavelengths. We illustrate the expected numbers of TP-AGB stars of different types in stellar populations covering a wide range of ages and initial metallicities, providing further details on the "C-star island" that appears at intermediate values of age and metallicity, and about the AGB-boosting effect that occurs at ages close to 1.6-Gyr for populations of all metallicities. The isochrones are available through a new dedicated web server.

Many stellar models present difficulties in reproducing basic observational relations of very low mass stars (VLMS), including the mass-radius relation and the optical colour-magnitudes of cool dwarfs. Here, we improve PARSEC models on these points. We implement the T -τ relations from PHOENIX BT-Settl model atmospheres as the outer boundary conditions in the PARSEC code, finding that this change alone reduces the discrepancy in the mass-radius relation from 8 to 5 per cent. We compare the models with multi-band photometry of clusters Praesepe and M 67, showing that the use of T -τ relations clearly improves the description of the optical colours and magnitudes. But anyway, using both Kurucz and PHOENIX model spectra, model colours are still systematically fainter and bluer than the observations. We then apply a shift to the above T -τ relations, increasing from 0 at T eff = 4730 K to ∼14% at T eff = 3160 K, to reproduce the observed mass-radius radius relation of dwarf stars. Taking this experiment as a calibration of the T -τ relations, we can reproduce the optical and near infrared CMDs of low mass stars in the old metal-poor globular clusters NGC 6397 and 47 Tuc, and in the intermediate-age and young solar-metallicity open clusters M 67 and Praesepe. Thus, we extend PARSEC models using this calibration, providing VLMS models more suitable for the lower main sequence stars over a wide range of metallicities and wavelengths. Both sets of models are available on PARSEC webpage.

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